Question

1. $y = \frac{3}{2}x$ and $y = -\frac{3}{4}x + 9$

solution:
check:

Explanation:

Step1: Set the equations equal

Since \( y = \frac{3}{2}x \) and \( y = -\frac{3}{4}x + 9 \), we set \( \frac{3}{2}x = -\frac{3}{4}x + 9 \).

Step2: Solve for x

Multiply all terms by 4 to eliminate denominators: \( 4\times\frac{3}{2}x = 4\times(-\frac{3}{4}x) + 4\times9 \), which simplifies to \( 6x = -3x + 36 \). Add \( 3x \) to both sides: \( 6x + 3x = 36 \), so \( 9x = 36 \). Divide by 9: \( x = 4 \).

Step3: Find y

Substitute \( x = 4 \) into \( y = \frac{3}{2}x \): \( y = \frac{3}{2}\times4 = 6 \).

Step4: Check the solution

Substitute \( x = 4 \) and \( y = 6 \) into \( y = -\frac{3}{4}x + 9 \): \( 6 = -\frac{3}{4}\times4 + 9 \), \( 6 = -3 + 9 \), \( 6 = 6 \), which is true.

Answer:

\((4, 6)\)